Focused wave interactions with a submerged flexible membrane (CCP-WSI Comparative Study 2 [formerly CCP-WSI Blind Test Series 4])

Description

The CCP-WSI Comparative Study 2 (formerly the CCP-WSI Blind Test Series 4) consists of three test cases involving a submerged flexible membrane subject to a focused wave event. In addition to these focused wave cases, there are also a number of additional cases to enable characterisation of the structural properties and the hydrodynamic conditions. These characterisation cases include: empty tank tests, i.e. generation and propagation of the focused wave events in isolation, without the structure present, and; static equilibrium tests, i.e. measurement of the membrane position/shape in equilibrium under the action of gravity (both submerged and subaerial). These test cases, and the experimental data, have been delivered as part of the Flexible Responsive Systems in Wave Energy (FlexWave) project [EP/V040367/1]

Experimental Set-up

The physical experiments were performed in the long ‘sediment’ flume in the COAST Laboratory at the University of Plymouth, UK. The flume is 35m long and 0.6m wide with a porous ‘beach’ at the downstream end. Waves are generated using a single wet-backed, piston wave maker (‘absorbing piston paddle’, 0.5m by 1.0m by Edinburgh Designs Ltd.). The water depth for the experiments was set to 0.7m (Figure 1).

The global coordinate system is defined with the z-axis running vertically (positive upwards) with z = 0 corresponding to the still water level. The x-axis runs in the direction of wave propagation (from the wave maker to the beach). The y-axis is defined according to the right-hand rule. The origin of the global coordinate system is located on the front face of the wave maker when at rest (19.36m upstream of the front edge of the membrane) on the centreline of the flume (Figure 1).

Experimental layout (incl. wave gauges)

The experimental layout, incl. the wave gauge (WG) positions, is presented in Figure 1. The locations of the wave gauges (WG) (in the global coordinate system) are indicated by black circles and summarised in Table 1

Table 1: Coordinates of wave gauges in global coordinate system (NOTE: all values in metres) [see Figure 1 for coordinate system definition]

	WG1	WG2	WG3	WG4	WG5	WG6	WG7	WG8
x coordinate	9.10	16.18	16.23	16.36	19.10	19.89	21.31	22.67
y coordinate	0	0	0	0	0	0	0	0

Membrane (and support frame)

Figure 1 shows the position of the membrane (and support frame) in the wave flume. The membrane is 0.998m long, 0.594m wide and 3mm thick (when unloaded). The membrane is clamped on all four sides using a bolted aluminium ‘sandwich’ frame. The details of the support frame are given below, however, due to the complexity of the experiment it is deemed acceptable for participants to assume the frame is rigid, even though this is not strictly true, and any discrepancies will be discussed in the analysis of the results. If participants would like to attempt to model the structural response of the support frame, as well as the membrane, we would be interested to receive results from simulations with both a rigid and with a flexible support frame if possible.

The aluminium frame beneath the membrane consists of 3mm thick, 998mm long, 13mm x 9mm angle section down the sides, welded to 568mm long, 20mm wide, 3mm thick flat bar running along the leading and trailing edges of the membrane/frame. The membrane is then clamped/sandwiched in place with 588mm long, 20mm wide, 3mm thick flat bar on the leading and trailing edges and 958mm long, 10mm wide, 3mm thick flat bar along the sides (Figure 2). This aluminium frame is then held in place (bolted) at each corner via a 30mm x 30mm x 30mm x 3mm stainless steel bracket and 30mm x 5mm stainless steel flat bar running vertically through the free-surface (Figure 2). The corners of the aluminium frame are assumed to be held rigidly by the stainless brackets and upright sections. However, the rest of the aluminium frame is relatively thin/flexible and cannot be assumed to be rigid.

The frame (and membrane) is positioned centrally in the flume (with a 3mm gap down each side), at a depth of 0.108m (from free-surface to top surface of aluminium cross members) (Figure 2) and with the front edge located 19.36m from the wave maker (when the membrane is in place WG6 is removed from the flume) (Figure 1).

Membrane deflection measurement

Figure 2 shows the positions of a series of membrane deflection measurements made using a laser distance sensor (labelled with an ‘L’ and a green diamond) throughout the test cases (the positions are fixed in the global coordinate system and summarised in Table 2).

Table 2: Coordinates of laser distance measurements in global coordinate system (NOTE: all values in metres) [see Figure 1 for coordinate system definition]

	L1	L2	L3	L4	L5	L6
x coordinate	19.605	19.858	20.108	19.858	20.108	20.108
y coordinate	-0.128	-0.128	-0.128	0.022	0.022	0.161

Support frame strain measurement

Figure 2 also shows the positions of a series of strain gauge sensors (labelled with an ‘S’ and an orange square) used throughout the test cases. Each strain gauge position (S) indicates the position of a pair of strain gauges (one on the upper piece/top face of the aluminium frame and one on the lower piece/bottom face of the aluminium frame. The strain gauges are fixed to the aluminium support frame (in the middle of the frame element). The positions of the strain gauges in the global coordinate system (when the frame is unloaded) are summarised in Table 3.

Table 3: Coordinates of strain gauges mounted on the (unloaded) aluminium frame in global coordinate system (NOTE: all values in metres) [see Figure 1 for coordinate system definition]

	S1	S2	S3	S4	S5
x coordinate	19.37	19.83	20.348	19.845	19.573
y coordinate	0.02	-0.289	0.007	0.289	0.289
z coordinate (top position)	-0.108	-0.108	-0.108	-0.108	-0.108
z coordinate (bottom position)	-0.117	-0.117	-0.117	-0.117	-0.117

Membrane material properties

The membrane in these cases is made of neoprene rubber. The material is used for hovercraft 'skirts' and has additives such as carbon black or micro-ceramic powers to improve abrasion resistance. As a result, the density, and stiffness, of the material (see Table 4) are greater than that of typical neoprene. To obtain the material properties, samples of the membrane material were tested using two alternative procedures based on the standards for ‘Coated Fabric Tensile Testing’ (ASTM D751) and the ‘Standard Test Methods for Vulcanized Rubber and Thermoplastic Elastomers’ (ASTM D412). The properties of the membrane in the linear response region (up to a strain of 5 - 6.5%) are given in Table 4. The properties of the membrane in the linear response region (up to a strain of 6.5%) are given in Table 4. NOTE: we recommend the Young’s modulus value from the ASTM D412 test (Table 4) but, for completeness, the value from ASTM D751 is ~6.23MPa.

Table 4: Membrane properties [see Figure 1 for positioning in global coordinate system]

	Value
Rest length [m]	0.998
Rest width [m]	0.594
Rest thickness [m]	0.003
Material density [kg/m3]	1500
Stiffness [N/m]	4676.92308
Young's modulus [MPa] (ASTM D412)	5.9
Poisson's ratio	0.4884

To provide more information regarding the properties of the membrane and enable calibration of the numerical models. The position/shape of the membrane has been measure when in static equilibrium (both in air and when submerged). Table 5 gives the vertical position, in the global coordinate system, of the top surface of the membrane at each of the laser distance sensor positions in Figure 2.

Table 5: Vertical position, in the global coordinate system, and deflection, from perfectly horizontal, of the top surface of the membrane at the six laser distance sensor locations (L) when in air and when submerged. (NOTE: all values in mm) [see Figure 1 for coordinate system definition and Figure 2 for sensor locations]

	L1	L2	L3	L4	L5	L6
z coordinate of membrane top surface (in air)[mm]	-135 ± 2	-141 ± 3	-139 ± 2	-151 ± 2	-143 ± 2	-131 ± 2
Deflection from perfectly horizontal membrane (in air)[mm]	-24 ± 2	-30 ± 3	-28 ± 2	-40 ± 2	-32 ± 2	-20 ± 2
z coordinate of membrane top surface (underwater)[mm]	-127 ± 2	-132 ± 1	-131 ± 1	-143 ± 3	-133 ± 3	-114 ± 6
Deflection from perfectly horizontal membrane (underwater)[mm]	-16 ± 2	-21 ± 1	-20 ± 1	-32 ± 3	-22 ± 3	-3 ± 6

Parameters used for wave generation

The waves, in each of the three blind test cases, are all generated using the EDL wave synthesiser and paddle control software. The displacement of the paddle is calculated using linear wave maker theory. 228 ‘fronts’ (components) evenly spaced between frequencies of 0.1 and 1.99167Hz (spacing = 0.025/3 Hz) are supply to the paddle control software based on a theoretical wave description. In these cases, the theoretical wave descriptions are all crest-focused (i.e. zero phase at focus location at focus time, ) NewWaves based on a JONSWAP spectrum (γ = 3.3) with a peak period, = 1.4s, a theoretical focus time, = 45s, and a theoretical focus location, = 19.9m upstream of the wave maker. The three wave definitions differ only by significant wave height, , and the crest amplitude, Acr, which is given by , where is the zeroth spectral moment and can be approximated according to . Table 6 summarises the theoretical parameters in the wave descriptions used for wave generation in each of the three focused wave cases 1CS2, 2CS2 and 3CS2. A file containing the parameters describing the 228 fronts in each case (e.g. 1CS2_fronts.txt) can be found in the ‘Resources’ section below.

Table 6: Parameters used for wave generation in the three blind test cases

	1CS2	2CS2	3CS2
Water depth [m]	0.7	0.7	0.7
Theoretical peak period, [s]	1.4	1.4	1.4
Theoretical significant wave height, [m]	0.015	0.03	0.04
Theoretical crest elevation, [m]	0.01394	0.02788	0.03717
Theoretical focus location, [m]	19.9	19.9	19.9
Theoretical focus time, [s]	45	45	45
Theoretical focus phase, [°]	0	0	0

In addition, for each of the test cases, the physical surface elevation measurements from an ‘empty tank’ test are supplied in the ‘Resources’ section (e.g. 1CS2_empty.txt) to enable participants to compare the accuracy of the wave generation/propagation in their models before adding the structure.

Physical Measurement Data

Submission Procedure

Relevant References

Resources